Plastic (Permanent) Deformation - 2016-09-09¢  Plastic (Permanent) Deformation...

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Transcript of Plastic (Permanent) Deformation - 2016-09-09¢  Plastic (Permanent) Deformation...

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 1

    (at lower temperatures, i.e. T < Tmelt/3)

    Plastic (Permanent) Deformation

    • Simple tension test:

    engineering stress, s

    engineering strain, e

    Elastic+Plastic at larger stress

    ep

    plastic strain

    Elastic initially

    permanent (plastic) after load is removed

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 2

    • Stress at which noticeable plastic deformation has

    occurred. when ep = 0.002

    Yield Strength, sy

    sy = yield strength tensile stress, s

    engineering strain, e

    sy

    ep = 0.002

    Note: for 2 inch sample

    e = 0.002 = z/z

     z = 0.004 in

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 3

    Room temperature

    values

    a = annealed

    hr = hot rolled

    ag = aged

    cd = cold drawn

    cw = cold worked

    qt = quenched & tempered

    Yield Strength : Comparison Graphite/ Ceramics/ Semicond

    Metals/ Alloys

    Composites/ fibers

    Polymers Y

    ie ld

    s tr

    e n

    g th

    , s

    y (M

    P a

    )

    PVC

    H a rd

    t o m

    e a s u re

    ,

    s in

    c e i n t e n s io

    n , fr

    a c tu

    re u

    s u a lly

    o c c u rs

    b e fo

    re y

    ie ld

    .

    Nylon 6,6

    LDPE

    70

    20

    40

    60 50

    100

    10

    30

    200

    300

    400

    500 600 700

    1000

    2000

    Tin (pure)

    Al (6061) a

    Al (6061) ag

    Cu (71500) hr Ta (pure) Ti (pure) a Steel (1020) hr

    Steel (1020) cd Steel (4140) a

    Steel (4140) qt

    Ti (5Al-2.5Sn) a W (pure)

    Mo (pure) Cu (71500) cw

    H a rd

    t o m

    e a s u re

    ,

    in c

    e ra

    m ic

    m a tr

    ix a

    n d e

    p o x y m

    a tr

    ix c

    o m

    p o s it e s , s in

    c e

    in

    t e n s io

    n , fr

    a c tu

    re u

    s u a lly

    o c c u rs

    b e fo

    re y

    ie ld

    . H DPE PP

    humid

    dry

    PC

    PET

    ̈

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 4

    Tensile Strength, TS

    • Metals: occurs when noticeable necking starts.

    • Polymers: occurs when polymer backbone chains are aligned and about to break.

    sy

    strain

    Typical response of a metal

    F = fracture or

    ultimate

    strength

    Neck – acts

    as stress

    concentrator

    e n g

    in e

    e ri n g

    TS

    s tr

    e s s

    engineering strain

    • Maximum stress on engineering stress-strain curve.

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 5

    Tensile Strength: Comparison

    Si crystal

    Graphite/ Ceramics/ Semicond

    Metals/ Alloys

    Composites/ fibers

    Polymers T e

    n s ile

    s tr

    e n

    g th

    , T

    S

    (M P

    a )

    PVC

    Nylon 6,6

    10

    100

    200

    300

    1000

    Al (6061) a

    Al (6061) ag

    Cu (71500) hr

    Ta (pure) Ti (pure) a

    Steel (1020)

    Steel (4140) a

    Steel (4140) qt

    Ti (5Al-2.5Sn) a W (pure)

    Cu (71500) cw

    L DPE

    PP

    PC PET

    20

    30 40

    2000

    3000

    5000

    Graphite

    Al oxide

    Concrete

    Diamond

    Glass-soda

    Si nitride

    H DPE

    wood ( fiber)

    wood(|| fiber)

    1

    GFRE (|| fiber)

    GFRE ( fiber)

    C FRE (|| fiber)

    C FRE ( fiber)

    A FRE (|| fiber)

    A FRE( fiber)

    E-glass fib

    C fibers Aramid fib

    a = annealed

    hr = hot rolled

    ag = aged

    cd = cold drawn

    cw = cold worked

    qt = quenched & tempered

    AFRE, GFRE, & CFRE =

    aramid, glass, & carbon

    fiber-reinforced epoxy

    composites, with 60 vol%

    fibers.

    Room temperature

    values

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 6

    • Plastic tensile strain at failure:

    Ductility

    • Another ductility measure: 100 x A

    A A RA %

    o

    f o -

    =

    x 100 L

    L L EL %

    o

    o f -

    =

    Lf Ao

    Af Lo

    Engineering tensile strain, e

    E ngineering

    tensile

    stress, s

    smaller %EL

    larger %EL

    % elongation

    % reduction in area

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 7

    Resilience

    • Ability of a material to store energy when deformed elastically.

    – Energy stored best in elastic region

    • If we assume a linear stress-strain curve,

    this simplifies to

     e

    es= y

    dUr 0

    • Modulus of resilience (Ur): strain

    energy per unit volume

    EE U

    yy

    yyyr 22

    1

    2

    1 2ss

    ses = 

      

     =

    • Note that:     332

    m

    J

    m

    mN

    m

    N PaUr =

     ==== s

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 8

    • Energy to break a unit volume of material

    • Approximate by the area under the stress-strain curve.

    Toughness

    Brittle fracture: elastic energy

    Ductile fracture: elastic + plastic energy

    very small toughness (unreinforced polymers)

    Engineering tensile strain, e

    E ngineering

    tensile

    stress, s

    small toughness (ceramics)

    large toughness (metals)

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 9

    True Stress & Strain • True stress:

    • True strain:

    iT AF=s

     oiT ln=e

    • If no volume change occurs during deformation,

    00 AA ii =

     es 

    sss = 

       

      =

     

       

     === 1

    0

    0

    000 

     ii iT

    A

    F AF

       e 

    e = 

       

      == 1lnlnln 0

    o

    oiT 

     

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 -

    True Stress & Strain • True stress

    • True strain

    iT AF=s

     oiT ln=e    e=e

    es=s

    1ln

    1

    T

    T

    • Engineering stress

    • Engineering strain

    0AF=s

    oe =

    • When necking begins,

    σ underestimated

    ε overestimated

    10

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 -

    True Stress & Strain • For some metals and alloys, the region of the

    true stress-strain curve from the onset of

    plastic deformation to the point at which

    necking begins may be approximated by

    s T = K e T  

    n

    “true” stress (F/A) “true” strain: ln(L/Lo)

    Strain hardening exponent: n = 0.15 (some steels) to n = 0.5 (some coppers)

    sT

    eT 11

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 12

    Elastic Strain Recovery

    S tr

    e s s

    Strain

    3. Reapply load

    2. Unload

    D

    Elastic strain

    recovery

    1. Load

    syo

    syi

  • Prof. Yo-Sep Min Fusion Technology of Chemical & Materials Engineering Lecture 10, Chapter 6 - 13

    Hardness • Resistance to permanently indenting the surface.

    • Large hardness means: -- resistance to plastic deformation or cracking in

    compression.

    -- better wear properties.

    e.g.,